Frontczak, Robert and Goy, Taras and Shattuck, Mark (2022) Fibonacci–Lucas–Pell–Jacobsthal relations. Annales Mathematicae et Informaticae, 55. pp. 28-48. ISSN 1787-6117
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Abstract
In this paper, we prove several identities involving linear combinations of convolutions of the generalized Fibonacci and Lucas sequences. Our results apply more generally to broader classes of second-order linearly recurrent sequences with constant coefficients. As a consequence, we obtain as special cases many identities relating exactly four sequences amongst the Fibonacci, Lucas, Pell, Pell–Lucas, Jacobsthal, and Jacobsthal–Lucas number sequences. We make use of algebraic arguments to establish our results, frequently employing the Binet-like formulas and generating functions of the corresponding sequences. Finally, our identities above may be extended so that they include only terms whose subscripts belong to a given arithmetic progression of the non-negative integers.
| Item Type: | Article |
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| Uncontrolled Keywords: | Generalized Fibonacci sequence, generalized Lucas sequence, Fibonacci numbers, Lucas numbers, Pell numbers, Jacobsthal numbers, generating function |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| Depositing User: | Tibor Gál |
| Date Deposited: | 21 Dec 2022 13:05 |
| Last Modified: | 21 Dec 2022 13:05 |
| URI: | http://real.mtak.hu/id/eprint/155441 |
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